Questions: The population standard deviation must be known to use T-test True False

Solution Steps

To determine whether the population standard deviation must be known to use a T-test, we need to understand the fundamental differences between a T-test and a Z-test. A T-test is typically used when the population standard deviation is unknown and the sample size is small, whereas a Z-test is used when the population standard deviation is known and the sample size is large.

• Understand the conditions under which a T-test is used.
• Compare these conditions to the statement given in the question.

The T-test is a statistical method used to determine if there is a significant difference between the means of two groups. It is particularly useful when the sample size is small (\( n < 30 \)) and the population standard deviation (\( \sigma \)) is unknown.

The T-test can be applied under the following conditions:

• The sample is drawn from a normally distributed population.
• The population standard deviation (\( \sigma \)) is unknown.
• The sample size is small (\( n < 30 \)).

The statement in question asserts that "the population standard deviation must be known to use a T-test." This is incorrect because the T-test is specifically designed for situations where the population standard deviation is unknown.

Final Answer